Relation between magnetization and Faraday angles produced by ultrafast spin-flip processes within the three-level A-type system

Ultrafast magneto-optical (MO) experiments constitute a powerful tool to explore the magnetization dynamics of diverse materials. Over the last decade, there have been many theoretical and experimental developments on this subject. However, the relation between the magnetization dynamics and the transient MO response still remains unclear. In this work, we calculate the magnetization of a material, as well as the magneto-optical rotation and ellipticity angles measured in a single-beam experiment. Then, we compare the magnetization to the MO response. The magnetic material is modeled by a three-level A-type system, which represents a simple model to describe MO effects induced by an ultrafast laser pulse. Our calculations use the density matrix formalism, while the dynamics of the system is obtained by solving the Lindblad equation taking into account population relaxation and dephasing processes. Furthermore, we consider the Faraday rotation of the optical waves that simultaneously causes spin-flip. We show that the Faraday angles remain proportional to the magnetization only if the system has reached the equilibrium-state, and that this proportionality is directly related to the population and coherence decay rates. For the non-equilibrium situation, the previous proportionality relation is no longer valid. We show that our model is able to interpret some recent experimental results obtained in a single-pulse experiment. We further show that, after a critical pulse duration, the decrease of the ellipticity as a function of the absorbed energy is a characteristic of the system

Equivalence between the semirelativistic limit of the Dirac-Maxwell equations and the Breit-Pauli model in the mean-field approximation

We demonstrate the equivalence between (i) the semirelativistic limit (up to second order in the inverse of the speed of light) of the self-consistent Dirac-Maxwell equations and (ii) the Breit-Pauli equations in the mean-field (Hartree-like) approximation. We explain how the charge and current densities that act as sources in the Dirac-Maxwell equations are related to the microscopic two-electron interactions of the Breit-Pauli model (spin orbit, spin-other-orbit, and spin-spin). The key role played by the second-order corrections to the charge density is clarified

Lagrangian approach to the semirelativistic electron dynamics in the mean-field approximation

We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in 1/c. Using a Lagrangian approach, we obtain the self-consistent charge and current densities that act as sources in the Maxwell equations. A physical interpretation is provided for the second-order corrections to the sources. The Maxwell equations are also expanded to the same order. The resulting self-consistent model constitutes a suitable semirelativistic approximation to the full Dirac-Maxwell equations

Foldy-Wouthuysen transformation applied to the interaction of an electron with ultrafast electromagnetic fields

By means of the Foldy-Wouthuysen transformation the nonrelativistic approximation of the external-electromagnetic-field Dirac equation to fifth order in powers of 1/m is obtained. Generalizing this result we postulate a general expression of the direct spin-field electronic Hamiltonian valid at any order in 1/m

How light modifies the electron-electron interaction under extreme conditions

In the domain of extreme light-matter interactions, we show that the electron-electron interaction can be modified coherently by the electric field of the light. The latter play the role of a third partner not only acting on the electrons individually but also on their mutual interaction. By using an original formalism based on the Foldy-Wouthuysen transformation and applied to the Dirac-Breit Hamiltonian in the presence of a time-dependent electromagnetic field, we obtain analytical expressions of new three-body light-matter interactions. (C) 2015 Elsevier B.V. All rights reserved

Diffusion centrale anomale des rayons X : application a des alliages metallurgiques

SIGLECNRS T 59267 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc